FK73,
I've never flown a PA38 so can't comment on the specifics.
However I've had the door open a number of times in a PA28. Apart from the irritating noise, it's a non event.
If you follow the guidance in the POH, it's very easy to close. Advice is basically to
1. slow down
2. Close all air vents (suprisingly important step)
3. Use lots of left rudder to get the airflow over the door
Doing this it is very simple to relatch.
If you don't mind the noise, then just keep going and ignore it!
I suspect that there is a similar proceedure in the PA38 POH. You should ready it and be prepared to do it next time if necessary.
dp